Difference between accepter and acceptor
I just think that acceptor is an older form of accepter. Though there are roughly parallel entries for them in the OED. Acceptor is certainly still in current use, but modern people I suggest would be inclined to use the accepter spelling.
So far as such instruments as Bills of Exchange are concerned, both are in use.
2004 Racing Post 7 May 8/2 A full list of acceptors will be issued tomorrow after the extended deadline, but one name confirmed yesterday was the Godolphin filly Punctilious.